"TROJAN FALL"

 

A galaxy should be a perfect hiding place. A hundred billion suns and a hundred thousand light-years form an appallingly large haystack in which to seek any such submicroscopic needle as a man, or even a planet. A photograph of the Milky Way, or, better, a projection of such a photograph, can give some idea of the sense of confusion which is experienced by anyone faced with the task of combing such a maze. 

That was La Roque's first impression, and his views of the galaxy had not been confined to photographs. Admittedly, he was used to interplanetary, rather than interstellar flight; but it is almost as easy to get lost inside solar systems as between them. So, when it became a matter of expedience for him to disappear from sight for a time, he decided quite abruptly that Sol's little family was too crowded. 

Getting a ship, even legally, was not too difficult; flight between Sol and the nearer stars was fairly common, and only the usual customs restrictions applied to private journeys. La Roque intended that his journey should be more private than usual. 

He purchased a craft; the event which made departure so urgent had left him with plenty of funds. She was about as small as a second-order flyer could be: a metal egg about seventy feet long and thirty in diameter at the widest point. She had the required two second-order converters, either capable of holding the ship and six hundred tons of additional mass in the necessary condition for interstellar flight above light-speed. Her actual capacity for freight was nowhere near that figure, of course. The converters consumed mercury, but could be modified to take any reasonably dense metal of low melting point. 

La Roque preferred the concealment of crowds, and for that reason chose to make his departure from the ever-busy Allahabad port. It was a little before midnight, on a July evening, that a pilot beam guided his ship beyond 66 the Earth's atmosphere; by 1 A.M. he had switched free, pointed the blunt nose of his ship at the center of the Milk Dipper's bowl, checked his personal equalizer, and shunted into second-order flight. The universe around him remained visible after a fashion, but aberration altered its appearance vastly. Every star swung forward; and at four hundred times the speed of light, they were all contained in a circular area, centered on his line of flight and a little over eight minutes of arc in radius. Sol was dead ahead, apparently, and prevented any possible view of his goal which might have been furnished by a telescope. 

La Roque was not a navigator, and knew no more astronomy than the average educated person of his time. Although the beacon stars Rigel, Deneb, and Canopus would all be visible in any part of the galaxy his ship was likely to reach, they were useless to him. His only hope of eventual return to the Earth lay in the device which, every hour, automatically cut the second-order fields for a split second and simultaneously photographed the heavens dead astern. Even that was likely to be useless if he crossed a region of low star density, where there would be no nearby, recognizable objects on the films to guide his return. He had had sense enough to realize this, and consequently had headed in the general direction of the galactic center. He was reasonably certain of finding a habitable planet; the star that lacked worlds was the exception rather than the rule. Earth-type worlds were rarer, but frequent enough to have forced the enactment of several regulations against unrestricted colonization. 

Having made the first step in his getaway, he settled down to figuring out the probable line of action of the law. It would, with luck, be a full month before his means of escape would be deduced, for it was known that he was not trained in cosmic navigation, and his ship would not be missed until sufficient time had elapsed for it to make a round trip to Tau Ceti, which he had indicated at Allahabad as his destination. It would take another day or two to compute his actual direction of departure, from the recording at the observatories which had presumably picked up his "wake." From then on, time would be short; any League cruiser of reasonable size could cover in two or three days any distance he could hope to put behind him in that month. It is an unescapable fact that the speed obtainable from a second-order unit is directly dependent on its size. 

Therefore, it was essential that a hiding place be found. A planet, where the ship could be buried or otherwise concealed, would present an impossible search problem to a hundred League ships—if there were no inhabitants to hold inconvenient memories of his landing. He might find such a world by random search, but the distance he could travel in his month of grace was limited; and, he realized, very few suns lay within that distance. He got out a set of heliocentric charts and began his search on paper. 

There is no excuse for him. His destination should have been planned before he left the ground—planned not only as to planet, but to location on the planet. He had always planned his "deals" with meticulous care; and had sneered at less careful colleagues whose failure to do so had resulted in more or less lengthy retirement to League reform institutions. It is impossible to say why he didn't see that the same principle might apply to interstellar flight. But he didn't. 

The reference volume that accompanied the charts was most helpful. Stellar systems were listed by right ascension, declination, and distance; so that he merely had to find the appropriate pages to find in a single group all the systems near his line of flight. 

There were twelve suns, in seven systems, lying with a light-year of his course, within the distance measured by a month's flight. Such a number was most surprising; chance alone would not insist on even one star within a cylinder of space two light-years in diameter and thirty-five long. Most of them, of course, were "dead" stars, detectable at only the closest range. Six of them had planetary systems; but the planets, without exception, possessed surface temperatures below the freezing point of mercury. 

That was unfortunate. To remain alive on any of these worlds would demand that he stay in the ship, and use power, for heat and light. Even such slight radiation as that would cause meant a virtual certainty of detection by even a cursory sweep of the planet on the part of a League cruiser. He had to find a place where the ship would remain at least habitably warm without aid from its own converters. He could do without light, he thought. 

The problem would not have bothered a pilot of even moderate experience, of course. The ship could easily be set in a circular orbit of any desired radius about one of the stars. Unfortunately, there is a definite relation between the mass of a star, the radius of the desired orbit, and the amount of initial tangential velocity required; and this simple relation was unknown to La Roque. Trial and error would be very unsatisfactory; the error might be unnoticeably small to start with, and become large enough to require correction when searchers were around. A worried frown began to add creases above La Roque's black brows as the little flyer raced on. 

The spot of light in the front vision plate grew paler as Sol, who provided most of its radiance, faded astern. Within a day, he was merely a bright star; in a week, dozens of others outshone him whenever La Roque cut the drive fields. Space, the runaway began to realize, was a terrifying lonely environment. Earth was beginning, in his memory, to assume a less forbidding aspect. 

Two days out, he passed the first of the seven systems. It was not visible, at half a light-year, even when the fields were off; the chart reference described it as a binary, both stars cool enough to have clouds of solid and liquid particles in their atmospheres, and neither emitting any visible radiation to speak of. The relative orbit was of almost cometary eccentricity, with a period of about seventy years. The suns had passed periastron about a dozen years before, without anyone's being greatly concerned. 

It was a dry collection of data, but it jogged La Roque's mind into recalling something. He had been picturing the result of an error in establishing an orbit, as being a spiral drop into the star he had chosen. Now he recalled that he would merely find himself in a slightly eccentric, rather than a circular, orbit; and if the eccentricity were not great enough to bring his periastron point actually within the star's atmosphere, it would be perfectly stable. 

The idea attracted him for a moment; even he could set up a passable concealment orbit. The possibility of being alternately too warm and too cold was unpleasant, but not forbidding. The system he was passing would not do, of course; he took it for granted that the perturbations produced by the companion star would nullify his attempts. However, four single suns were among those he had looked up along his course, and were within easy reach. 

It remained to choose one of the four. Any reasonable and normal person would have without hesitation laid a course for the nearest; La Roque, under the elemental motivation that sent an incognito Hitler to Borneo rather than Switzerland, chose the farthest. Perhaps his gambling spirit had something to do with the choice; for there was actually some doubt that he would reach the star before a League cruiser would come nosing along his wake into detection range. 

From where he was, the runaway could not lay a direct course for his chosen hideout. His knowledge of solid geometry and trigonometry was so small that all he could do was to continue on his present course until the proper heliocentric distance was attained, then stop, put Sol exactly on his beam, hold it there while he turned in the proper direction, and again run in second-order flight for a certain length of time—dead reckoning pure and very simple. By thus reducing his goal position to a known plane —or near plane; actually the surface of a sphere centered on Sol—he could get the course of his second leg by simply measuring, on a plane chart, the angle whose vertex was the point in the sky toward which he had been driving, and whose sides were determined, respectively, by some beacon star such as Rigel or Deneb, and the star of his destination. He dragged out a heliocentric chart and protractor, and set to work. 

Time crawled on. The nearer stars, on the trail photographs, drifted sluggishly toward Sol. La Roque found a photometer, and managed to obtain with its aid a check on his distance from the Solar System. He spent much of his time sleeping. There was nothing to read except the charts, astrographical and planetographical references, and the numbers on the currency leaves whose gathering had necessitated his departure from Earth. The latter kept up his morale for a while. 

Second-order pilotage is not difficult; it depends chiefly on proper aiming of the ship before cutting in of the converters. There is practically no tendency to drift from the original heading; in fact, it is impossible to turn without cutting the fields and re-aligning the vessel's axis. Actually, the ship will follow the arc of a circle whose radius depends to some extent on the power of the generators, but in any case is so enormous that a "local" interstellar flight may be considered rectilinear. La Roque's intended flight path was so short that his ignorance of short-order field technology made no difference. An experienced navigator, planning a flight across the galaxy, or to one of the exterior systems, would have to forecast and allow for the "drift" caused by generators of any given make and power. 

One by one, the star systems La Roque had rejected dropped behind. Each time he fought the temptation to turn aside and seek refuge. Days turned into weeks, three of them, from the time he had chosen his destination. By the most generous estimate, his margin of clearance from the law was growing narrow, when he cut the fields at—according to his reckoning—twenty-eight point seven seven four seven light-years from the Solar System. 

He snapped on plate after plate, looking around in every direction. A fifth-magnitude star on the cross wires of the rear plate was, of course, Sol. He looked for Deneb, but Cygnus was too badly distorted by a parallactic variation of nine parsecs to permit him to identify its alpha star with certainty. Orion was recognizable, since he had been moving more or less directly away from it and all its principal stars were extremely distant; so he decided to use Rigel to control his direction. 

He zeroed the cross wires of one of the side plates and, using the gyros, swung the ship until Sol was centered on that plate. Rigel was, conveniently, visible on the same plate; so he snapped a switch which projected a protractor onto it, and swung the ship again until Rigel was on the proper—according to his measures—radius. Using the plate's highest power, he placed the two stars to four decimals of accuracy, released the gyro clutches, and cut in the second-order fields before friction at the gyro bearings could throw off his heading. 

His arithmetic said he had eight hours and thirty minutes of flight to his destination. Experience would have told him that his chances of stopping within detection range of his goal were less than one in a hundred thousand; as it was, the chief worry that actually disturbed him was whether or not there was risk of collision. Not too surprising! In dead reckoning, the novice navigator makes a tiny point and says, "Here we are." The junior makes a small circle and says the same. The experienced navigator lays the palm of his hand on the chart and says, "We ought to he here." And La Roque's was the deadest of dead reckoning. 

He cut the fields five seconds early, and looked expectantly at the forward plate. There should have been a crimson, glowing coal half a billion miles ahead of him. Of course there wasn't.

For a moment he was completely bewildered; but, as he was a reasonable creature, it was only for a moment. He had evidently made a mistake; not necessarily a very large one. He had already obtained the spectrobolometric curve of the star, and fitted the appropriate templets into the detectors. There would be no confusion; no sun having anything like that energy curve could be picked up by those instruments at more than a few billion miles. The galaxy is crowded with such expiring stars, it is true; but a "crowded" star system still contains a vast amount of empty space. 

'La Roque "sat down"—strapped himself into a seat, since he was weightless—and planned again. He would have to sweep out the space around him, stopping at least every ten billion miles—every two minutes—for at least the ten seconds the instruments would require to sweep the celestial sphere. A volume of space that could be covered in a reasonable time would have to be decided on, and the decision adhered to. If he started a random search, he might as well open the ports. 

The results of some more arithmetic bothered him. A really appalling number of five-billion-mile cubes could be packed into an area that looked very small on the chart. He finally worked the other way—allowing himself one hundred hours for the search. He decided he could cover a cube roughly one hundred and forty billion miles on a side, in that time. He realized sadly that his dead reckoning error could easily be several times that. 

He was no quitter, however. He was beginning to realize the chances against him—not merely against his escape, but against his survival; he had long since realized his error in tackling a job about which he knew next to nothing; but having decided on his course of action, he embarked on it without hesitation. He started the sweep. 

His patience lasted admirably for the first hour. It stood up fairly well for the second. By the end of the third, the smooth routine of flight—cut-wait-and-watch-flight was growing ragged. When the clock and radiometer dials began to blur, and the urge to break something grew almost irresistible, he called it a day and slept two or three hours. After the second period, he couldn't sleep either. 

Really, he was undeservedly lucky. One of the radiometers reacted after only eighteen hours of blind search. His near hysteria vanished instantly, washed away in a flood of relief; and with hands once more reasonably steady he swung the little ship until the emanations registered on the bow meter. He noted the strength of the reading, cut in the second-order fields for five seconds, and read the dial again. He knew the inverse square law, at least; he figured for a moment, then drove forward again for eleven more seconds, and cut the fields between twenty and thirty million miles from the source of the radiation. 

It was visible to the naked eye at that range, which, in a way, was unfortunate. Had it not been, La Roque would have had a few more happy minutes. As things were, he took one look at the forward plate, and for the next ninety seconds used language which should really have been recorded for the benefit of future sailors. He had some excuse. The star was listed in the chart reference as single; La Roque had chosen it for that reason. However, plainly visible on the plate, revolving evidently almost in contact, were two smoky red suns—a close binary system. 

Of course, no one would normally be greatly interested. The Astrographic Survey vessel which had covered the section had probably swept past fifty billion miles out, and noted the system's existence casually as its radiometers flickered. Size? Mass? Companions, if any? Planets? Who cared! 

La Roque, of course. 

The stars were red dwarfs, small and dense. They would have been seen to be irregular variables, if anyone had looked long enough; for their surface temperatures were so low that "cirrus" clouds of solid carbon particles formed and dispersed at random in their atmospheres. The larger sun was perhaps a hundred thousand miles in diameter, the other only slightly smaller. Their centers were roughly half a million miles apart, and the period of revolution about eight hours. In spite of their relatively high density, there were very noticeable tidal bulges on both. 

All these facts would have been of absorbing interest to an astronomer seeking data on the internal structure of red dwarf stars; La Roque didn't know any of them, and at first didn't give a darn. He was wondering how a stable orbit could be established close enough to this system to keep him from freezing without using ship's power. The near-circular one he had planned was out; it would have had to be less than a million miles from a single sun of such late type, and the doubling of the heat source wasn't much help. 

He thought of doubling back to one of the other systems which the chart had said to be single; but the nerve-racking search and disappointment he had suffered the first time made him hesitate. It was while he hesitated that memory came to his aid. 

There had been an episode in his experiences which had occurred on Hector, one of the Trojan asteroids. Circumstances had caused him to remain there for some time, and a friendly jailer had explained to him just where Hector was and why it stayed there. It was in the stability point at the third corner of an equilateral triangle whose other corners were Sol and Jupiter; and though it could—and did—wobble millions of miles from the actual point, gravitational forces always brought it back. 

La Roque looked out at the twin suns. Could his ship stand the temperature at the Trojan points of this system? More important, could he stand it? 

He could. His instruments gave the energy distribution curve of the suns; one of the reference charts contained a table that turned the curves into surface temperatures. He was able to measure the distance between the centers of the suns, from the scale lines on the plate and his distance, which he knew roughly. Half a million miles from the surface of a star whose radius was fifty thousand miles and whose effective radiating temperature was a thousand degrees absolute, the black-body temperature was, according to his figures, about thirty degrees Centigrade. The presence of two stars made it decidedly warmer, but his ship was well insulated and the surface highly polished. It would eventually reach an equilibrium temperature considerably above that of an ideal black body, but it would take a long time doing so. 

It seemed, then, that the Trojan point was the best place for him. He could find it easily enough; getting the centers of the stars sixty degrees apart would put him at the right distance. He could find the proper plane by moving around until the two suns appeared to move across each other in straight lines. It would not take long; by varying his distance from the system he could, in a few minutes, observe it through half a revolution. 

It took him, in fact, less than an hour to find the orbital plane of the suns. It took him five and a half hours of first-order acceleration at one gravity to get rid of the hundred and twenty mile per second velocity difference between Sol and this system—fortunately, the chart had mentioned the high relative velocity, or La Roque would never have thought of such a thing. In a way, he didn't mind the necessity; it was good to have weight for the first time in nearly a month. He was, of course, a little worried at the amount of time consumed; he wished he had not wasted so much of the commodity in putting Sol so far behind. 

He cut the first-order drive the instant his clock told him the speeds should be equal, headed for the twin suns, and hopped for his Trojan point. Since moving bodies were involved, he had to make five legs out of the short trip—he failed to allow for the short period of the system and the fact that he started the first leg several light-hours from his goal. 

He got there eventually, however. He suddenly realized that he would have to use first-order power again, to give his ship something like the proper orbital velocity; but even he was able to understand the proper magnitude and direction of this new vector; the only unjustified assumption he had to make was that the suns were of equal masses, and this happened to be nearly the case. He wasn't too worried; he understood that in a Trojan orbit such small variations are opposed, not helped, by the gravity of the primary bodies. He was quite right. 

He cut all his power except the detector relay currents, which did not radiate appreciably. To these he connected an alarm, and set them to synchronize with the low-frequency waves which form the "wake" of a vessel cruising at second-order speeds. Then, abruptly feeling the reaction of the past days, he drifted over to a "bunk," moored himself, and was instantly asleep. 

It is impossible to say just how long he slept; he was exhausted mentally and emotionally, and when weightless the human body can approach a condition near to suspended animation, if given the chance. It couldn't have been for very many hours, but the alarm rang for minutes before its sound penetrated to his consciousness. When it did, he had to wait several moments before he could move a muscle. 

Recovered at last, he unmoored himself and kicked his body across the narrow cabin to the instrument board, and cut the alarm, cursing. He had forgotten that the bell would radiate, and was not sure that the hull would shield its waves. The detectors were reacting violently, the needles wobbling rapidly from positive to negative limits. He knew that a ship had driven past in second-order flight, but that was as far as he could interpret the readings. It would have required an expert to compute the speed, type, and distance of the ship creating the disturbance. 

After a few minutes, the needles quieted. La Roque remained at the board, judging that the ship had not left for good. He was right. The disturbances started again half an hour later, and kept up for hours thereafter—sometimes so feeble as to cause a barely visible quiver of the needles, sometimes slamming them against the stop pins with audible clicks. La Roque was incapable of reading any meaning except changing distance into this phenomenon. 

The "wake" of a ship in straight-line, second-order flight consists of a few low-frequency electromagnetic waves, the wave-front being, as can easily be seen, coneshaped, with the ship at the apex. The cone expands radially at the speed of light, and its tip moves forward with the ship—in the case of a military craft, at anywhere up to something like a million light velocities. 

If the ship is not in straight-line flight, but cutting its fields and changing direction every few minutes or seconds, the shape of the wave front becomes rather complex. A standard search path spirals around the surface of a torus, and after a few hours the traces of such a flight would be the despair of a competent mathematician, let alone an amateur at a comparatively fixed observation post. The space for billions of miles around that binary sun was quivering with crisscrossing wave fronts. Each set the needles of La Roque's detectors quivering in tune as it passed him, and each quiver brought beads of sweat to the runaway's brow. His own ship, he realized, had left similar fronts; and he had shaved his margin of escape much too fine. Had they been given a week, or even three or four days, for expansion at the speed of light, he could have ceased to worry about their being used to trail him. 

He wondered just what the searchers would do. They must have trailed him directly to this system, as he had expected. They might try to find an inactive ship in space, but La Roque doubted that such a search would be practical unless there existed detection instruments unknown to the general public. 

He wondered if the system contained any planets, to add to the searchers' difficulties. He himself had seen none, and none was listed on the chart; but they would have been nearly invisible in the dim light of the twin suns, and La Roque's faith in the chart had dropped a long way. If there were any, they would be a real help; they would have to be searched mile by square mile. 

But the question of prime importance was, how long would the pursuers stay? Certainly, if they had the patience they could outwait him, for their food supply would outlast his; but for all they knew he might have met with a fatal accident, or encountered an organized outlaw base—either could easily happen. If he refrained from radiating long enough, they might decide further search futile. He could do that; the darkness didn't bother him particularly, and the ship was warm enough—a little too warm, in fact. Evidently his figures had not been exact. 

Eventually the detectors stopped reacting, and La Roque started waiting. He was still perspiring, less from worry now than from actual warmth. The ship was becoming uncomfortable. He removed his outer clothing and felt better for a while. 

Time crawled on—rapidly decelerating, in La Roque's opinion. He had nothing to do except notice his own discomfort, which was on the increase. He cursed the ship's builders for failure to insulate it properly, and the men who had computed the tables he had used to obtain the probable temperature at this distance from the suns. He didn't bother to curse his own arithmetic. 

Once he was almost on the point of driving farther out, hoping the pursuing ship had gone; but a flicker from one of the detectors made him change his mind. He hung and sweated; and the temperature mounted. 

It must have been a hundred and fifty degrees Fahrenheit when he finally gave in. He could have stood more in the open—anyone could—but the air-conditioning apparatus had been stopped along with everything else, and the air in the ship was approaching saturation. With that fact considered, he held out remarkably well; but eventually his will power gave out. He kicked his way feebly back to the board and snapped on the vision plates. 

He lacked the energy to curse. For moments he could only stare in shocked horror at the plates—and realize how misdirected his previous denunciations had been. There was nothing wrong with his ship's insulation; the wonder was that it had held out so well. One of the suns—he never knew which—completely filled the front, top, and port plates with a blaze of sooty crimson; he must have been within thirty or forty thousand miles of its surface. His hand darted toward the activating switch of the second-order drivers, and was as quickly checked. They would only send him straight forward, into the inferno revealed by the front plate. The ship must be turned. 

He started the gyros, careless now of any radiation that might result. The control knobs were hot to the touch; and a smell of burning oil reached his nostrils as the gyros wound up to speed. The ship abruptly shuddered and began to gyrate slowly, as one of them seized in its bearings. He watched tensely as the vessel went through a full rotation, his hand hovering over the board; but not once was the glow in the forward plate replaced by the friendly darkness of space. The ship was spinning on its longitudinal axis. 

The other gyros were working. He tried to turn the vessel with them. The result was to shift the axis of spin about thirty degrees—and increase its rate tenfold as another of the heavy wheels, spinning at full speed, jammed abruptly. Centrifugal force snatched him away from the board and against one wall; he shrieked as his flesh touched hot metal, and kicked violently. His body shot across the room, reaching the other side at about the same time his previous point of contact was carried around by the ship's rotation. 

The specks of carbon cirrus on the front plate were describing circles now—circles whose size was visibly increasing. For part of each turn the nose was now pointing into space; La Roque tried to fight his way back to the board to take advantage of one of those moments.

He might have made it, in spite of the agony of his burns, but the overstrained insulation had done its best. It failed; and failed, of all places, over the water tanks that lined part of the hull. The tanks themselves offered only token resistance as steam pressure suddenly built up in them. La Roque never knew when scalding water shorted the control board, for a jet of superheated steam had caught him just before he reached it. 

On the enforcement cruiser, a man straightened up from a plotting board. 

"That does it, I think," he said. "He was using heavy current for a while, probably trying to turn out with his gyros; then there was a flash of S.H.F., and everything stopped. That must have taken out his second-order, and he'd have had to use about sixty gravities of first-order to pull out of that spot. I wonder what he was doing so close to those suns." 

"Could have been hiding," suggested a second pilot. "He might have thought the suns would mask most of his radiation. I wonder how he expected to stay there any length of time, though." 

"I know what I'd have done in his place," replied the first man. "I'd have put my ship into a Trojan position and waited the business out. He could have lasted indefinitely there. I wonder why he didn't try that." 

"He probably did." The speaker was a navigator, who had kept silent up to this point. "If a smart man like you would do it, a fellow like that couldn't be expected to know any better. Have you ever seen a planet in the Trojan points of any double sun? I'll bet you haven't. That Trojan solution works fine for Sol and Jupiter—Sol is a thousand times the more massive. It would work for Earth and Luna, since one has about eighty times the mass of the other. But I have never seen a binary star where the mass ratio was anywhere near twenty-five to one; and if it's less, the Trojan solution to the three-body problem doesn't work. Don't ask me why; I couldn't show you the math; but I know it's true—the stability function breaks, with surprising sharpness, right about the twenty-five-to-one mass ratio. Our elusive friend didn't know that, any more than you did, and parked -his ship right in the path of a rapidly moving sun." He shrugged his shoulders, and turned away. "Live and learn, they say," he finished, "but the difficulty seems to lie in living while you learn."